Kernels for the Vertex Cover Problem on the Preferred Attachment Model

Abstract

We examine the behavior of two kernelization techniques for the vertex cover problem viewed as preprocessing algorithms. Specifically, we deal with the kernelization algorithms of Buss and of Nemhauser & Trotter. Our evaluation is applied to random graphs generated under the preferred attachment model, which is usually met in real word applications such as web graphs and others. Our experiments indicate that, in this model, both kernelization algorithms (and, specially, the Nemhauser & Trotter algorithm) reduce considerably the input size of the problem and can serve as very good preprocessing algorithms for vertex cover, on the preferential attachment graphs.

This research was supported by the EU 6th FP under contract 001907 (DELIS). The first author was partially supported by the Distinció per a la Promoció de la Recerca de la GC, 2002.